Price is the key point of it. The 1070 should be relatively more expensive, as a result is better than the 1060 in all aspects, the normal 1070 that is...
The mini version, still got the same amount of power inside it, it's just... Mini. Smaller, reduced amount of cooling system, therefore louder due the increased charge on a single or fewer coolers and sometimes even hotter. But as power is concerned, it's the same.
So, in addition to the comment above, IMHO i'd get the 1070 as well if the price isn't much and you're fine with a little bit of noise